The formatting of this problem makes it very difficult to read.
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AmzotiDec 23 '12 at 6:08

There is probably a proof in Elaydi's textbook on discrete dynamical systems. I don't have access to my copy at the moment. It's also possible that typing "saddle node bifurcation" into Google will turn up a proof for you.
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Gerry MyersonDec 23 '12 at 16:58

thanks Gerry-myerson i found it in this book
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Maisam HedyellooFeb 4 '13 at 18:22